School of Mathematics and Statistics - Theses
Now showing items 1-10 of 155
Selected problems in enumerative combinatorics: permutation classes, random walks and planar maps
In this thesis we consider a number of enumerative combinatorial problems. We solve the problems of enumerating Eulerian orientations by edges and quartic Eulerian orientations counted by vertices. We also find and prove ...
Unsteady motion of small particles in fluid: from autonomous propulsion to the interrogation of liquid-solid interfaces
Fluid flows at micro- and nanometre length scales are governed by physical processes that are quite different to their macroscale counterparts. When these flows interact with suspended solid particles, a rich array of ...
The isoperimetric problem in block designs
This thesis focuses on the problem of determining the isoperimetric numbers of Levi graphs of balanced incomplete block designs. We study two versions of this: the vertex-isoperimetric number and the edge-isoperimetric ...
Statistical models for the location of lightning-caused wildfire ignitions
Lightning-caused wildfire is a significant concern for fire management agencies worldwide. Unlike other ignition sources, lightning fires often occur in remote and inaccessible locations making detection and suppression ...
Quantifying interactions between nanoengineered particles and cells
Nanoengineering has recently emerged as a promising technology for the understanding, treatment, and diagnosis of disease. One of its most compelling potential uses is in the design of particles with controlled interactions ...
The exact asymptotics of large deviation probabilities in the multivariate boundary crossing problem
For a multivariate random walk with i.i.d. jumps satisfying the Cramer moment condition and having a mean vector with at least one negative component, we derive the exact asymptotics of the probability of ever hitting the ...
Chevalley groups and finite geometry
This thesis explores the possible use of Schubert cells, Schubert varieties and flag varieties in finite geometry, particularly in regard to the question of these objects might be a source of understanding of ovoids or ...
Combinatorial enumeration and the Bethe Ansatz
This thesis focuses on combinatorial enumeration of lattice paths using the Constant Term method. In particular we make use of the Bethe Ansatz, an Ansatz given by a linear combination of solutions to the free ``no ...
Extinction in branching processes with countably many types
Multitype branching processes describe the evolution of populations in which individuals give birth independently according to a probability distribution that depends on their type. In this thesis, we consider the extinction ...
Networks of interacting stochastic fluid models
The focus of this thesis is the study of Markov modulated fluid models in the performance modelling of ad hoc telecommunications networks – that is networks where nodes communicate via multi-hop routes as there is no central ...